Information Geometry of Complex Hamiltonians and Exceptional Points
arXiv:1307.4017 · doi:10.3390/e15093361
Abstract
Information geometry provides a tool to systematically investigate parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian, then there can be phase transitions where dynamical properties of the system change abruptly. In the vicinities of the transition points, the state of the system becomes highly sensitive to the changes of the parameters in the Hamiltonian. The parameter sensitivity can then be measured in terms of the Fisher-Rao metric and the associated curvature of the parameter-space manifold. A general scheme for the geometric study of parameter-space manifolds of eigenstates of complex Hamiltonians is outlined here, leading to generic expressions for the metric.
17 pages, invited contribution for a Special Issue on "Distance in Information and Statistical Physics"
References in corpus (9)
- The physics of exceptional points
- Visualization of Branch Points in PT-Symmetric Waveguides
- A non-Hermitian symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
- Mixed-state evolution in the presence of gain and loss
- Bypassing the bandwidth theorem with PT symmetry
- Coulomb analogy for nonhermitian degeneracies near quantum phase transitions
- Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
- Eigenvalue structure of a Bose-Einstein condensate in a PT-symmetric double well
- Berry Phases and Quantum Phase Transitions
Cited by in corpus (32)
- Biorthogonal Quantum Mechanics
- A Geometric Perspective on Quantum Parameter Estimation
- Essay: Where Can Quantum Geometry Lead Us?
- General Theory of Spontaneous Emission Near Exceptional Points
- Quantum metrology for a general Hamiltonian parameter
- Geometry and response of Lindbladians
- Experimental measurement of the divergent quantum metric of an exceptional point
- Exceptional Bound States and negative Entanglement Entropy
- Ultimate precision of multi-parameter quantum magnetometry under the parallel scheme
- Control-enhanced sequential scheme for general quantum parameter estimation at the Heisenberg limit
- Quantum metric and wavepackets at exceptional points in non-Hermitian systems
- Quantum metrology beyond the Quantum Cramér-Rao theorem
- Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems
- Non-adiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice
- Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime
- Higher-order Time-Symmetry-Breaking Phase Transition due to meeting of an Exceptional Point and Fano Resonance
- Generalized Quantum Geometric Tensor in a Non-Hermitian Exciton-Polariton System
- Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics
- Dynamics of finite dimensional non-hermitian systems with indefinite metric
- Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
- Estimation of general Hamiltonian parameters via controlled energy measurements
- Probing eigenfunction nonorthogonality by parametric shifts of resonance widths
- Geometrical aspects of the multicritical phase diagrams for the Blume-Emery-Griffiths model
- Fluctuation-enhanced quantum metrology
- Adiabatic Transformations in Dissipative and Non-Hermitian Phase Transitions
- Quantum geometrical effects in non-Hermitian systems
- Programmable non-Hermitian photonic quantum walks via dichroic metasurfaces
- Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
- Simulation of exceptional-point systems on quantum computers for quantum sensing
- Multi-block exceptional points in open quantum systems
- Complex extension of Wigner's theorem
- PT symmetry and the evolution speed in open quantum systems